Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#430 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | C2×D4 |
| commutator | C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C4 | C23×C23 |
| socle | C2×C23 | C2×C4⋊C4 |
| prime radical | C23×C23 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,31,29,32,27,37)(26,33,36,38,34,39,35,30);(24,26,27,35,29,34,28,36)(25,30,31,33,32,38,37,39);(26,34)(30,38)(33,39)(35,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 111);